Elliptical curve cryptography image encryption scheme with aid of optimization technique using gravitational search algorithm

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by  Ramireddy Navatejareddy, Muthukuru Jayabhaskar, Bachala Sathyanarayana

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 25, No. 1, January 2022, pp. 247~255
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v25.i1.pp247-255  247

Elliptical curve cryptography image encryption scheme with aid
of optimization technique using gravitational search algorithm

Ramireddy Navatejareddy1, Muthukuru Jayabhaskar1, Bachala Sathyanarayana2
1Department of Computer Science Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, India
2Department of Computer Science and Technology, Sri Krishnadevaraya University, Ananthapur, India

Article Info ABSTRACT
Article history: Image encryption enables users to safely transmit digital photographs via a
wireless medium while maintaining enhanced anonymity and validity.
Received Jun 21, 2021 Numerous studies are being conducted to strengthen picture encryption
Revised Oct 6, 2021 systems. Elliptical curve cryptography (ECC) is an effective tool for safely
Accepted Nov 23, 2021 transferring images and recovering them at the receiver end in asymmetric
cryptosystems. This method's key generation generates a public and private
key pair that is used to encrypt and decrypt a picture. They use a public key
Keywords: to encrypt the picture before sending it to the intended user. When the
receiver receives the image, they use their private key to decrypt it. This
Elliptical curve cryptography
paper proposes an ECC-dependent image encryption scheme utilizing an
Gravitational search
enhancement strategy based on the gravitational search algorithm (GSA)
Optimization
algorithm. The private key generation step of the ECC system uses a GSA-
Image encryption based optimization process to boost the efficiency of picture encryption. The
MSE image's output is used as a health attribute in the optimization phase, such as
PSNR the peak signal to noise ratio (PSNR) value, which demonstrates the efficacy
of the proposed approach. As comparison to the ECC method, it has been
discovered that the suggested encryption scheme offers better optimal PSNR
values.
This is an open access article under the CC BY-SA license.

Corresponding Author:
Ramireddy Navatejareddy
Department of Computer Science Engineering, Koneru Lakshmaiah Education Foundation
Vaddeswaram, Guntur, Andhra Pradesh, 522502, India
Email: [email protected]

1. INTRODUCTION
The increased reliance on computers to process data and distribute it over virtually linked networks
has heightened the need for protection. Information protection has become a concern as a result of
developments in network technologies in today's modern environment. If the digital era progresses, we will
be able to obtain knowledge explicitly and simply communicate it by photographs [1]. It was not done
without any pitfalls, such as unauthorized access to these records and illicit copying. The importance of
secret transmission in protecting classified information against risks and misuse cannot be overstated. In
multimedia systems, image protection is a crucial and commanding problem [2], [3]. Encryption and
decryption of data have developed into the optimal method for ensuring the confidentiality and legitimacy of
data. There will eventually be a significant test, when hazards and weaknesses develop in lockstep with
advancements [4]. Nowadays, various methods have been developed to provide security while also
increasing the amount and usage of computing resources [5]. Image encryption strategies enable us to alter a
unique image to another (encoded) image that is not easy; consequently, to keep the image hide among
customers, or in other words, to ensure that no one can gain access to the substance without a decryption
key [6]. Image encryption strategy attempt to turn an image into a difficult-to-understand image that is highly
Journal homepage: http://ijeecs.iaescore.com
2 4 8  ISSN: 2502-4752
sensitive for users, implying that no one will access the content without a decryption key. Only the main
identified individual has access to the initial picture magnitude. For cryptographic techniques, the majority of
standards, such as hardware and applications, use the public key methodology. Elliptical curve cryptography
(ECC) is asymmetric key cryptography, which implies that the encryption and decryption keys are not the
same [7], [8]. A key pair is used in public key cryptography, with one serving as the private key and the other
as the public key [9], [10]. The public keys are distributed to all people, and only the person who is
participating in the conversation recognizes the private key. ECC, unlike secret key cryptography, is ideal for
systems where a protected channel to relay the private key is not available [11], [12]. ECC is a nearly modern
public key cryptosystem that offers higher thresholds, lower mathematical difficulty, smaller key sizes, and
greater computational efficiency [13], [14]. The protection of such photos is becoming increasingly critical as
digital products communicate over accessible networks. Some benefits of evolutionary optimization
algorithms include the ability to optimize the fitness role of independent variables [15]. Essentially, these
methods use iterative trial and error improvement, analogous to how living organisms adapt and evolve to
find the best fitness under defined conditions [16], [17]. Particle swarm optimization (PSO) is a simple-to-
implement population-based stochastic strategy that has seen a lot of success in solving real-world
continuous optimization problems in preesent years. PSO and differential evolution (DE) are two strength
based stochastic search methods that are commonly used to solve optimization problems in many research
and engineering fields [18], [19].

2. LITERATURE REVIEW
Naskar and Chaudhuri [20] proposed a stable encryption strategy for digital images in 2014; it can
also be used for any digital data images (e.g. audio, image, and text). A block of hidden bytes is ciphered
using bit-wise XORing and flipping, and then each ciphered byte is moved inside N locations (N is the secret
byte size). This is a method that combines replacement and carrying using dynamic substitution box (SBOX)
and transcription box (TBOX). The cryptosystem's key is very big, which makes it more secure against brute-
force attacks. Furthermore, main statistical analysis, sensitivity analysis and differential attack analysis
demonstrate the author's established strategies high acceptability. Kumar et al. [21] suggested the first double
stage arbitrary matrix affine cypher paired with digital wavelet transformation for RGB picture encryption
and decryption in 2013. The encryption process is simple in their system, but the decryption process is more
difficult, particularly when there is no additional knowledge about the right keys or the possible correct
remote monitoring and control (RMAC) parameter settings. The writers also offer a security overview as well
as a study of their methodology to that of others. It reveals that their correctly decrypted picture has a very
low mean square error (MSE), indicating that the method decrypts with very little knowledge loss. Proposed
strategy can be used to send RGB picture data over insecure channels easily and safely. Loukhaoukha et al.
[22] suggested a new picture encryption strategy based on the Rubik's cube theorem in 2012. In this article,
picture conservation is of special concern. The Rubik's cube theory is used to scramble the initial picture. The
XOR operator is extended to columns and rows of the scrambled picture using two hidden keys as the first
step in this principle. The same key is flipped and added to the hidden images even rows and columns. The
proposed algorithm's robustness against various forms of attacks, such as mathematical and differential
attacks, was demonstrated by a systematic numerical study (visual testing). Kumar and Anil [23] developed a
system for developing ECC for file formats such as audio, video, and image in 2011. It's often used to
compress files of the same kind. Security-constrained data may be hidden and retrieved using the software
available. The protocols in the elliptic curve methodology are framed and thought to be impossible to
recognize the discrete strategy of random ECC peaces with respect to a public recognized base point. The
complexity of the issue is determined by the curve scale. In general, there are two people involved in the
encryption and decryption processes, one on the encryption area and the other on the decryption area. Data is
submitted not only in image form, but also in audio, video, and image form. Bh et al. [24] addressed
Koblitz's approach for representing a message as a point and vice versa in 2010. The execution time for
encoding and decoding functions is unaffected by the values of a, b, and p. (domain parameters ECC). For
various values of the ECC domain parameters, the encoding execution period varies. For various values of a,
b, and p, the execution period for decoding is constant. As opposed to encoding, decoding takes a fraction of
the time.
ECC has established itself as a promising cryptographic technique [25]. The National Institute of
Standards and Technology (NIST) defined the elliptic curve random generator as a method for grouping
random digits based on curves. The random age stage is determined by a publicly available key and a
changing point G, which serves as the generator of a curve used to generate random configurations.
Advanced encryption standard (AES) is then coupled to these configurations, securing self-assertive keys for
image encryption. AES in close proximity to widely spread random provides an illustrious encryption
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Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752  249

technology. Shankar and Lakshmanaprabu [26] suggested a homomorphic encryption scheme based on ant
lion optimization (ALO).To increase the level of security, an approach called ALO is announced. The strong
encrypted image is displayed in terms of maximum entropy with this ALO. Ewees et al. [4] proposed onset
of blood lactate accumulation (OBLGOA), an upgraded form of the grasshopper optimization algorithm
(GOA) that incorporates the opposition-based learning (OBL) methodology. The study examined the
implementation of the suggested OBLGOA by conducting six test strategies that included 23 benchmark
capacities and 4 building difficulties. The results revealed that the suggested computation produced superior
results than those frequently obtained through accurate recommendations in this area. Finally, the researchers
concluded that when compared to cutting-edge algorithms, OBLGOA calculation can produce aggressive
results in optimization design problems.

3. PROPOSED METHODOLOGY
The suggested image encryption system is utilized to transfer a private initial image from the sender
to the recipient. The RGB pixel values are recognized from the base image, and a different RGB matrix is
produced using their pixel parameters. After that, the picture is separated into blocks earlier the encryption
phase begins. The elliptical curve cryptography technique is used to encrypt each block's separate matrix.
Following that, each block's pixel value is substituted with the new pixel value. This method is used to obtain
the scrambled image while still concealing the initial image. Following the completion of the encryption
procedure, the encrypted picture is decrypted using the reverse encryption technique [27]. The GSA
algorithm's optimization strategy was extended to the private key generation method during the decryption
process. The image's output is taken as a health value to be considered as the Peak Signal to Noise Ratio
(PSNR) value after the optimized key generation phase is completed. When the highest PSNR value is found,
it is used as the private key's optimum health and ideal key value [28], [29]. When the decryption step is
complete, the final yield picture is compared to the base image to assess accuracy using the PSNR,
correlation coefficient (CC) and mean square error (MSE). The original picture is safely exchanged using this
process, and the original information's confidentiality is retained.

3.1. Elliptical curve cryptography (ECC)
ECC is one some kind procedure for applying public key cryptography in asymmetric key
cryptography [30], [7]. Based on this procedure, the maximal limit is calculated with a fixed base point and
the prime number function, and the encryption follows: The basic ECC equation is shown in (1).

𝑦2 =𝑥3+𝑎𝑥+𝑏 (1)

Here a and b are the integers. The intensity of encryption depends on the created key in every cryptographic
operation. Two forms of key generation are available in the proposed process. Firstly, public key is produced
for encrypting the message from the receiver end and secondly, to create a private key to decrypt the original
picture at the reception end. If the value “P” is any some point on the curve, select a random integer number
“H”, which is a private key, in the area of “1 to n-1”, then the public key “Q” is generated as (2).

𝑄 =𝐻×𝑃 (2)

3.1.1. Encryption method
In the encryption part of the procedure, every color band of the input picture is divided into the
blocks. These four blocks are encrypted by the proposed encryption method. The total count of the blocks is
presented asF(i, j). Where and i and j are the number of rows and columns of the blocks of the image [12],
[31]. The pixels P(i, j)and P (i1, j)and the point is obtained in (3) and (4).
x y

𝐶 =𝐻×𝑃 (3)
1 𝑒

𝐶 =(𝑃,𝑃 )+𝐶 (4)
2 𝑥 𝑦 1

3.1.2. Decryption method
In the decryption part of the procedure, the private key (H) is used to decrypt the information and
the point C of (5) is used to decrypt the pixel point;
3

Elliptical curve cryptography image encryption scheme with … (Ramireddy Navatejareddy)
2 5 0  ISSN: 2502-4752
𝐶 =𝐻×𝐶 (5)
3 1

𝐶 =𝐶 −𝐶 (6)
𝑖𝑗 2 3

In this process the C represents the final result. In the procedure of decryption, the secret key (H) is
ij
produced by the proposed cat swarm optimization (CSO) technique, which gives the best optimized values
compared to the existing ECC technique.

3.1.3. Gravitational search algorithm
Gravitational search algorithm (GSA) is an observational technique focused on Newton's laws of
universal gravitation, which was earlier recognized in 2009 [32], [33]. The strategy follows gravitational
law's inductive reasoning: “For any two objects, a force is drawn to the other object that is directly
proportional to their mass and inversely proportional to their square distance.” The gravitational force of any
two nodes is based on the gravity theorem as presented in (7).

𝐹(𝑡)=𝐺(𝑡)𝑀1𝑀2 (7)
𝐷(𝑡)2

Where, M and M are the mosses of the two nodes and Dis the distance between the nodes. The
1 2
gravitational constant G at the time of t instant is given by (8).

𝐺(𝑡)=𝐺(𝑡 )𝑒𝑥𝑝(−𝛼𝑡/𝑇 ) (8)
0 𝑓𝑖𝑛𝑎𝑙

In this expression α is the positive constant, G(t )is the gravitational constant at the time instant of t and
0 0
T is the total search time. The cost function value is heavily influenced by the gravitational constant at
final
time t and the original masses. A node with a higher mass is a stronger node. Similarly, lighter mass denotes
a weaker node. The new defined variable related to the jth node is given by (9).

𝑚 (𝑡)= 𝐶𝑗(𝑡)−𝐶𝑗𝑤𝑜𝑟𝑠𝑒(𝑡) (9)
𝑗 𝐶𝑏𝑒𝑠𝑡(𝑡)−𝐶𝑤𝑜𝑟𝑠𝑒(𝑡)
𝑗 𝑗

Where 𝐶(𝑡) is the cost function of the jth node at the iteration instant of t. 𝐶𝑤𝑜𝑟𝑠𝑒(𝑡) represents the worst
𝑗 𝑗
cost function and 𝐶𝑏𝑒𝑠𝑡(𝑡) represents the best cost function. The mass and acceleration of the jth node are
𝑗
given by (10) and (11).

𝑀 (𝑡)= 𝑚𝑗(𝑡) (10)
𝑗 ∑𝑛𝑗=1𝑚𝑗(𝑡)

𝑎 (𝑡)=𝐹𝑗,𝑘(𝑡) (11)
𝑗,𝑘 𝑀𝑗(𝑡)

For various values of k=1, 2, 3…. P and j=1, 2, 3…N, the variable N represents the number of nodes and the
variable P represents the number of parameters to be optimized within the node. F (t), indicates the force
j,k
of the particles at the position of x (t) and M (t) represents the mass of the jth particle. The velocity of
j,k j
kth parameter of jth node at t+1 iteration is given by (12).

𝑣 (𝑡+1)=𝑟𝑎𝑛𝑑 𝑣 (𝑡)+𝑎 (𝑡) (12)
𝑗,𝑘 𝑗 𝑗,𝑘 𝑗,𝑘

Where rand represents a random number varying between 0 and 1. The final position of kth parameter in
j
jthnode at the instant of t+1 is given by (13).

𝑥 (𝑡+1)=𝑥 (𝑡)+𝑣 (𝑡+1) (13)
𝑗,𝑘 𝑗,𝑘 𝑗,𝑘

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The set of values k is used to obtain the best solution and in every iteration it is updated. The complete
best
process of obtaining best values is depicted in Figure 1.

Figure 1. Flow chart representation of GSA

3 RESULTS AND DISCUSSION
This part of paper presents the experimental findings on the suggested image encryptions and
optimization technique. The suggested ECC Image Encryption with GSA Optimizationwas implemented in
MATLAB 2018 using an i5 processor and 8 GB RAM system setup. The Tables 1 and 2 illustrate two
representative input images, namely Lena and boat. Encrypt the image of the relevant input images and then
decrypt them. Following decryption, the final yield image is compared against to the genuine image to
demonstrate the proposed algorithm's performance, using quality metrics such as MSE, CC and PSNR values
for each image.

Elliptical curve cryptography image encryption scheme with … (Ramireddy Navatejareddy)
2 5 2  ISSN: 2502-4752
Table 1. ECC image encryption with GSA optimization technique for Lena image
Reconstructed
Input Image Color band Share creation Combined Sharing Encryption Decryption
Output
R1

G1

B1

R2

G2

B2

Table 2. ECC image encryption with GSA optimization technique for boat image
Share Combined Reconstructed
Input Image Color band Encryption Decryption
creation Sharing Output
R1

G1

B1

R2

G2

B2

Table 3 compares the proposed ECC with GSA method to the ECC technique using several critical
quality indicators such as MSE, CC and PSNR values for images Lena, boat, Barbara, fingerprint and eye
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images. According to the table, the proposed method improved the image quality because its PSNR value is
more than that of the ECC algorithm. The comparison study indicates that the suggested picture encryption
approach achieves an acceptable level of security. It clearly indicates that the proposed strategy outperforms
the ECC approach. Table 4 provides the comparative results analysis of the presented WSA-ECC modelwith
existing CSO-fruit fly optimization (FFO)-ECC. From the Table 4, itis evident that the GSA-ECC model has
obtained better performance compared to CSO-FFO-ECC model. On the applied image 1 Lena, the GSA-
ECC model has resulted in a higher PSNR of 60.04 dB at the same time, on the applied image 2, the GSA-
ECC model has resulted in a higherPSNR of 59.3 dB.

Table 3. Comparative analysis of ECC and proposed ECC with GSA method
Input Method PSNR MSE CC
ECC 45.94 1.67 0.9
GSA-ECC 60.04 0.065 1

ECC 46.07 1.62 0.9
GSA-ECC 59.24 0.078 1

ECC 46.23 1.56 0.9
GSA-ECC 59.3 0.077 1

ECC 46.61 1.43 0.9
GSA-ECC 58.64 0.87 1

ECC 46.35 1.52 0.9
GSA-ECC 57.91 0.105 1

Table 4. Comparison of the proposed GSA-ECC method to existing Method CSO-FFO-ECC in terms of
MSE and PSNR
ProposedGSA-ECC CSO-FFO-ECC [1]
Input Image
MSE PSNR MSE PSNR
0.065 60.04 0.088 58.68

0.077 59.3 0.092 58.49

4 CONCLUSION
The research presents an ECC-based picture encryption strategy that is optimize using GSA
methodology. It is demonstrated unequivocally that the suggested approach produces a higher-quality image
with an average PSNR value of 60.04 between the genuinel and output images. The mean square error is
likewise reduced in all images, which means that almost all photos have a correlation coefficient of nearly 1.
Histogram and correlation coefficient analyses make it abundantly evident that the encryption process
remains unaltered and maintains the secret image's confidentiality. Comparative investigation demonstrates
that the suggested strategy outperforms ECC in terms of encryption quality and PSNR values. In the future,
we will examine the suggested method's resilience to various forms of attacks such as salt and pepper,
filtering, cropping, and blurring.
Elliptical curve cryptography image encryption scheme with … (Ramireddy Navatejareddy)
2 5 4  ISSN: 2502-4752
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Indonesian J Elec Eng & Comp Sci, Vol. 25, No. 1, January 2022: 247-255
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752  255

BIOGRAPHIES OF AUTHORS

Ramireddy Navatejareddy had obtained his B.Tech in information technology
from Jawaharlal Nehru Technological University, Hyderabad, Andhra Pradesh, India in 2007
and M.Tech in Computer Science & Engineering from Visvesvaraya Technological
University, Karnataka State, India in 2010. He has teaching experience of 10+ Years in the
department of Computer Science & Engineering. Currently he is pursuing Ph.D in Koneru
Lakshmaiah Education Foundation-KLEF. His research areas of interest are computer
networks & secuiry, IoT, cloud computing. He can be contacted at email:
[email protected].

Muthukuru Jayabhaskar has 7+ years of industry and 7+ years of teaching
experience and has interests in real time issues in Networks which lead to research in Network
and Data Security and further implementation of different security techniques like
cryptography and signcryption. He published 20 papers in reputed journals. He completed his
Ph.D on Elliptical Curve Cryptography Implementation Approaches for Efficient Smart Card
Processing from Sri Krishnadevaraya University. He can be contacted at email:
[email protected].

Bachala Sathyanarayana as 31 years of teaching experience and has interests
in the area of security issues in Computer Networks and internet of things. He published 57
papers in reputed journals. He served as a chair. He guided 16 Ph.D, 5 M.Phil students and
guiding 3 Ph.D students. Currently working as professor in the department of Computer
Science and technology in Sri Krishnadevaraya University, Ananthapuramu, A.P, India. He
can be contacted at email: [email protected].

Elliptical curve cryptography image encryption scheme with … (Ramireddy Navatejareddy)